Predicting the Coupling Properties of Axially-Textured Materials

Abstract

A description of methods and computer programs for the prediction of “coupling properties” in axially-textured polycrystals is presented. Starting data are the single-crystal properties, texture and stereography. The validity and proper protocols for applying the Voigt, Reuss and Hill approximations to estimate coupling properties effective values is analyzed. Working algorithms for predicting mentioned averages are given. Bunge’s symmetrized spherical harmonics expansion of orientation distribution functions, inverse pole figures and (single and polycrystals) physical properties is applied in all stages of the proposed methodology. The established mathematical route has been systematized in a working computer program. The discussion of piezoelectricity in a representative textured ferro-piezoelectric ceramic illustrates the application of the proposed methodology. Polycrystal coupling properties, predicted by the suggested route, are fairly close to experimentally measured ones.

Procedures for reducing large datasets of crystal orientations using generalized spherical harmonics

“…The GSH are known to be the most compact Fourier basis requiring the least number of Fourier coefficients for describing ODF and the dependence of various material properties on ODF (Fuentes-Cobas et al, 2013;Kalidindi et al, 2009;Knezevic and Kalidindi, 2007) because they can be symmetrized to reflect various crystal and sample symmetries. The adopted notations for the symmetrized GSH functions are _ _ T ln l ðgÞ for cubic,…”

“…Crystallographic texture (also called the orientation distribution function, or the ODF) is an important feature of the microstructure in polycrystalline materials known to have a strong influence on the anisotropy of various material properties (Adams and Olson, 1998;Bhattacharyya et al, 2015;Bunge, 1993;Fromm et al, 2009;Fuentes-Cobas et al, 2013;Jahedi et al, 2014;Knezevic et al, 2014a;Kocks et al, 1998). Therefore, anisotropic material models must consider the distribution of crystal orientations.…”

Texture and Electromagnetic Coupling Properties

“…Polycrystal properties coefficients are linear combinations of single crystal ones' times the ODF expansion coefficients. Specific algorithms for polycrystalline magnetostriction, consistent with the general theory, are presented below in the description of the program Magnetostriction_Texture.py . The CIMAV Crystal Physics Group works to introduce in MPOD the option of estimating average properties of textured polycrystals using programs based on the Bunge method.…”

“…Dealing with coupling properties special precautions must be taken. The analysis in ref . is summarized as follows.…”

The plasticity of highly oriented nano-layered Zr/Nb composites

“…When subject to bulk metal forming processes, such as rolling, polycrystalline metals develop texture [1,2]. Texture affects both mechanical [3][4][5] and functional properties [6,7]. As such, control of texture evolution during processing is an approach often used to help attain target properties and eventual performance [8][9][10][11][12].…”